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Jewish Calendar Accuracy

77% of the holy days in the past 100 years have been on the wrong date according to the Jewish calendar. These errors are caused by inaccuracies in the math of the Jewish calendar that have added up over time. (Test this yourself)

Despite this extremely high error rate, the Jewish calendar is often praised for being accurate. How is this possible? One example is the following quote from Avraham Yaakov Finkel that is used in a number of Church of God articles [1] to espouse the accuracy of the Jewish calendar.

The calculation of the calendar was transmitted to the sages in an unbroken chain going back to Moses. … According to the ancient calculations, the exact time between one new moon and the next is 29 days, 12 hours, and 793 chalakim ‘parts of an hour’ (the hour is divided into 1080 parts). In other words, one lunar month has 29.53059 days. It is interesting to note that according to NASA (National Aeronautics and Space Administration); the time between one new moon and the next is 29.530588 days. Of course, NASA has at its disposal the most advanced and sophisticated telescopes and computers. Nevertheless, the difference between NASA’s figures and that used by Hillel II, which originated more than 3000 years ago, is .000002 or two millionths of a day, calculated for the period of one month. Avraham Yaakov Finkel, The Essence of the Holy Days: Insights from the Jewish Sages 1993, p. 141

A very small error?

The error in question is on the average length of time between the conjunction of two new moons. From one new moon conjunction to the next is called a lunation or synodic month, and the average length of time for a synodic month is about 29.53058751 days. This same period of time is called the “molad” in Jewish calendar calculations. Since the measurements used for the initial Jewish calendar’s molad are from the Greek astronomer Hipparcus from over 2 thousand years ago, their measurement wasn’t as accurate as we have now and the synodic month has been getting shorter this entire time.

According to Finkel the Jewish calendar’s molad is only off by 2 millionths of a day from his claim of NASA’s measurement (Finkel’s book was published in 1993) of the average synodic month, which has about -.17 seconds per month difference. But even an error of -.17 seconds per month would mean that the Jewish calendar gave the wrong dates 23% of the time in the last 100 years. (Test this yourself)

But Finkel's number "2 millionths of a day", or -.17 seconds per month, itself is inaccurate.

Another number that is often quoted,  which is closer to the truth, is half a second of error per month. But despite this amount of error the Jewish calendar is still considered “remarkably accurate” by this COGWA article on their Young Adult Blog.

How accurate is the Hebrew calendar?

According to Judaism 101, the average lunar month on the Hebrew calendar and the average lunar month calculated by modern astronomers are only different by “about half of a second. That is quite remarkably accurate.”

COGWA Young Adult Blog, Leap Day, Leap Months and Other Notable Times

How accurate is the Jewish calendar actually?

About "half a second" (-.5 seconds) and "2 millionths of a day" (-.17 seconds) per month seem like insignificant differences until you realize this difference is multiplied 10s of thousands of times. For the year 2018 this error is multiplied 71,440 times.

Also, there is a 66% difference between -.5 seconds and -.17, which is a significant amount, so which number is correct? Can tiny fractions of a second really make any difference when calculating the dates for the holy days? (Test this yourself)

Dr. Irv Bromberg, an expert in the math of the Jewish calendar and the Sanhedrein's reference for the math of the Jewish calendar wrote this.

The Mean Synodic Month is currently about 3/5 second or 9/50 of a part [3 1/3 seconds] shorter than the traditional molad interval... Dr. Irv Bromberg, Moon and the Molad of the Hebrew Calendar

3/5 of a second difference is -.6 seconds. But a more accurate formula from Dr. Irv Bromberg shows that the value is closer to -.57 seconds.

Traditional Molad [lunation/synodic month] Period = 29 days 12 hours 793 parts = 29 days 12 hours 44 minutes 1 part = 29.53059414 days.
...
Apparent Mean Synodic Month at present = 29.53058751 solar days = 0.57 seconds shorter than Molad period.

Dr. Irv Bromberg, Apparent Mean Synodic Month vs. Lunation

In addition to this disparity, lunar months are becoming shorter every year. This means the accuracy of the Jewish calendar is degrading more as time passes.

Can these seemingly minute difference really matter all that much? Here’s a summary of the results of these errors on the dates for the holy days for the last 100 years.

  • -.57 seconds off = 77% error rate
  • -.6 seconds  off =  82% error rate
  • -.17 seconds off = 23% error rate

You can test this yourself using the Jewish Calendar Accuracy Test.

References